Lab work in photonics.

Lab work in photonics.

Detectors and noise.

1 Photodetection noise sources 1

2 Infrared detector characteristic measurement 21

3 CMOS sensor 41

4 Thermal camera 53

lense.institutoptique.fr | Deuxième année | Photonique S8

Engineer - 2

year - S8 -Palaiseau

Version : February 5, 2019

Year 2018-2019

B 1

Photodetection noise sources

Version: February 5, 2019 Prepare the question P1 before the session.

Contents

1 Objectives . . . . 1

2 Measuring noise . . . . 2

3 Amplification noise . . . . 5

4 Thermal resistance noise . . . . 9

5 Photon noise . . . . 11

6 Noise reduction . . . . 14

7 Short guidelines for the redaction of the report . . 18

Appendix 1. Bode diagrams of the amplifiers . . . . 19

Appendix 2. The spectrum analyser . . . . 20

1 Objectives

At the end of this lab session, you are expected to be able to:

• differentiate between an offset (typically a dark current) and a noise;

• measure a noise amplitude,i.e.to be able to:

– use an electrical spectrum analyzer;

1

– convert quantities expressed indBm_@1Hzand inW/Hz,

– explain how the Spectrum Analyzer (SA) performs a measure- ment;

– determine the influence of important parameters in any noise measurement, and in particular, the influence of the bandwidth (ENBW);

– evaluate the uncertainty of the measurement;

• break down the different contributions (amplification noise, thermal noise, photon noise) to the total noise;

• propose a measurement method for each kind of noise;

• verify if a detection system is limited by photon noise;

• justify the term “photon noise”.

The objective of the first three parts of this lab is to study the main sources of noise present in any optical sensing system: the amplification noise, the thermal noise, and especially the photon noise.

The photon noise is related to the quantum nature of light. It has long been considered as a fundamental limitation. Under certain very partic- ular conditions , it is nevertheless possible to fall below the photon noise limit, also known as the “standard quantum limit”, as has been demon- strated for the first time in 1985¹. The last part presents an experiment that reduces the photon noise to a value below the standard quantum limit.

You are asked to fill up a table during the lab in order to record your measurements and verify their validity.

2 Measuring noise

2.1 Statistical approach

A noise is a random process. When measuring a noise, we want to deter- mine its statistical properties, in particular its variance, also known as its rms value. By definition :

V_rms² = Z

v²p(v)dv

1Slusheret al.,Phys. Rev. Lett.55, 2409 (1985).

2. MEASURING NOISE 3 wherep(v)is the density of probability of the process. It is not always known, but it can be estimated, experimentally measured.

2.2 Time-domain measurement

For all stationary and ergodic stochastic signals, we consider that the temporal statistical properties are the same as the ensemble statistical properties. This is the case for all kind of noise we will study here.

Therefore, with an oscilloscope, one can measure the Root Mean Square voltageV_rmsofv(t)(mean value is zero) defined by:

V_rms² = lim

T7−→+∞

1 T

Z

[T]

v²(t)dt

This is the definition of the total power of a signal. This is also the temporal standard deviation for a noise:

V_rms² =σ²_v= v²(t)

∀t

2.3 Frequency-domain measurement

The same RMS voltage measurement can be done in the frequency do- main. With a spectrum analyzer (SA), we can measure thePower Spec- tral Density(PSD)of an electric signal. The PSD is defined by:

PSD(f) = 1 R_SA lim

T7→+∞

2 T

D|vf_T(f)|²E

(1.1) for frequenciesf >0. vT is the signalv(t), limited to the interval[0T], fvT(f)is its Fourier Transform.R_SAis the input resistance of the SA. The PSD is expressed inW/Hz.

The rms noise voltage, normalized at1 Hz,vn(nfornoise),is:

v_n(f) =p

R_SA·PSD (f)in V/√ Hz.

We get the total power, so the RMS voltage by integrating the PSD over all frequencies :

V_eff² =R_SA Z +∞

0

DSP(f)df = Z +∞

0

v²_n(f)df

2.4 Link between the autocorrelation function of a noise and the PSD

Thanks to the Parseval theorem, we know that the total power of a signal does not depend on the representation (time or frequency) of the signal.

There is a connection between those two, given by the Wiener-Khintchine theorem. The PSD can be obtained from the autocorrelation function cv(τ) =hv(t)v(t−τ)iby a Fourier Transform :

2

R_SAcv(τ)→^FTPSD(f) And forτ= 0,thus leads to:

V_eff² =σ²_v=c_v(0) =R_SA Z +∞

0

DSP(f)df

2.5 White noise. Filtering.

The noises studied in this lab are very chaotic signals. There is no correla- tion between their value at timetand at timet+τ. Their autocorrelation function, cv(τ), is zero for all the values of τ except0: cv(τ) = 0except inτ = 0. The PSD is then constant for all frequencies. By analogy with optics, the expression of "white noise" is used to characterize them. A white noise is a mathematical model. Its variance is infinite. We usually talk about white noise in a given bandwidth if the PSD is constant in this frequency bandwidth.

Furthermore, the measurement of a noise is always limited by a given bandwidth which can be the scope bandwidth, the resolution bandwidth of the spectrum analyzer, the bandwidth of a filter, .... The measured rms voltage is then :

V_eff² = Z ∆f

0

v²_n(f)df =v²_n(f) ∆f

wherevn(f)is the rms noise voltage normalized at1 Hz, and is supposed to be constant in the bandwidth of analysis∆f.

So, measuring a noise consists in giving its rms voltage nor- malized at 1 Hz AND the bandwidth in which this power is mea- sured !

Be aware that two noises may have the same PSD and very different time traces. An example of this is given on the figure 1.1 :

3. AMPLIFICATION NOISE 5

time

time b₁t

b₂t

frequency Power Spectral Density

DSPb₂=DSPb₂

V

V

s

s Hz

W/Hz

Figure 1.1: Two different noises with the same PSD.

P1 What is the shape of these two noise histograms? Are their autocor- relation functions identical ? Which one is a white noise? Which one is a Gaussian noise?

3 Amplification noise

We need a low-noise and high gain amplifier to measure the thermal noise of a resistance or the photon noise.

However, the amplifier produces its own noise. The aim of this part is to measure the amplifier noise.

This amplifier noise is the output noise of the complete electronic sys- tem, added to an amplified signal. Its rms value is notedV_ampli,out.In or- der to compare amplifiers with different gain and bandwidth values, the input rms noise voltage normalized at1 Hz, is given. We consider then a noise generator at the input of an amplifier as shown in figure 1.2. We have to measure the rms noise voltagev_n,ampli (inV/√

Hz) of this white noise.

G ,f

v_{n ,ampli} vout

Figure 1.2: Input white noise model.Gis the amplifier gain and∆f is its bandwith

The circuit diagram we will use is drawn on the figure 1.3: It corre- sponds to « Ampli 1 » aluminium box, with a grounded input. To shortcut the entrance, use the box of resistances connected directly to the Ampli 1 box input, and choose theR= 0 Ωposition. The amplifier is powered by batteries (±12 V) to avoid additional noise.

ampli

Ve Vs

+15V

-15V R

Ampli 1 : Bruit thermique

Figure 1.3: Amplifier noise and thermal noise measurements circuit.

3.1 Noise measurement with an oscilloscope.

Observe the output signal with the oscilloscope (1or2 mV/division).

Q1 Observe the output voltage when you change the time scale. Does the shape of the noise seem compatible with a Gaussian white noise?

Q2 Measure approximatelyVpeak to peak of the noise observed on the os- cilloscope. Assuming this noise is a Gaussian noise, we know that : Vpeak to peak ≈6V_RMS.

Deduce the Root Mean Square (RMS) value (V_{ampli, out}) of the amplifier output voltage.

Furthermore we suppose that the amplifier gain is 300and constant over a bandwidth of∆f = 1,5 MHz(Bode Diagram in appendix)

Q3 What is the relationship betweenv_n,ampliandV_ampli,out? Deduce from your measurement the rms input voltage noise of the amplifier v_n,ampli and compare to theAH0013datasheet typical value:vn,AH1003 = 2 nV/√

Hz

3. AMPLIFICATION NOISE 7

3.2 Noise measurement with a spectrum analyzer

With a spectrum analyzer (Tektronix 2712 for example), one can measure the PSD of the noise (scheme in appendix).

The SA displays the electric power of its input voltage inWor indBm signal, dissipated in its input resistanceR_SA= 50 Ω.

If this signal is a sine wave at frequencyf₀ v(t) =√

2V_rmssin (2πf₀t+φ), the displayed power isP(f0) =^V_R^rms2

SA

.

If this signal is periodic, the SA displays the power of each spectral component of the signal

If this signal is a noise, the SA displays the signal PSD, integrated over the resolution bandwidthδf = RBWaroundf₀:

P(f₀) = 1 R_SA

Z f0+^δf₂ f₀−^δf₂

v_n²(f)·df(in W) If we assume that the PSD is constant overδf:

P(f0) = 1

R_SA·v_n²(f0)·δf(inW)

Dividing this value by the resolution bandwidth, the SA measures the PSD (inW/Hz) of the electrical signal :

PSD (f0) =P@1 Hz(f0) = v²_n(f0)

R_SA (in W/Hz)

HOW TO USE THE SPECTRUM ANALYZER FOR NOISE MEASUREMENT

Choice of the span Menu : MKR/FREQ 7 FREQUENCY START STOP

0 FREQ START ENTRY Choose0 Hz

1 FREQ STOP ENTRY Choose 400 kHz for a measurement at 200 kHzor2 MHzto plot the Bode diagram of the amplifier Resolution Bandwidth Menu : RBW

You can choose the resolution bandwidth (RBW) and check that you clearly understand what is the influence of the RBW on the noise spectrum.

Reference level Menu : REF LEVEL

Changing the REF LEVEL will change the value of the top line of the screen. REF LEVEL may be chosen from20and

−70dBm. Set the Ref level to−30dBm.

Measurement of the power spectral density Menu : APPL 2 Noise normalized : If you do so, the spectrum analyzer

will measure and display indBm@1 Hz(on the top right cor- ner of the screen) the power spectral density of noise at a frequency corresponding to the marker.

Reminder: Remember thatdBmis a logarithmic power unity. ’m’ means that the reference is 1 mW. A power indBm is given by: PdBm = 10 log_{10 1 mW}^P

where P is expressed in mW. So, 0dBm is 1 mW,

−30dBmis1µW,−60dBmis1 nW, etc.

A PSD is given indBm_{@1 Hz}:P_{@1 Hz,dBm}= 10 log ^P_{1 mW}^{@1 Hz}

Connect the output of the amplifier to the spectrum analyzer input.

MeasureP@1 Hz(200 kHz)indBm,the amplifier noise output power spec- tral density at200 kHz.

Q4 Using Excel, calculate the corresponding noise voltage,v_n,out(200 kHz), at the amplifier output expressed inV/√

Hz. The SA input resistance is R_SA= 50 Ω.

Q5 Determine the value of the amplifier gain at a frequency of200 kHz from the Bode diagram of the amplifier given in Appendix. Deduce the rms input noise voltagev_n,ampli. Compare it to the value obtained in the previous section and to the datasheet value for the low noise amplifier AH0013:v_n,AH1003 = 2 nV/√

Hz.

Q6 Observe the output noise voltage of the amplifier for a larger span of frequencies from0to2 MHz. Is it a white noise? Why? Compare to the Bode diagram (ampli Johnson noise) given in appendix. Explain why we can measure the Bode diagram of the amplifier by this method.

4. THERMAL RESISTANCE NOISE 9 Check your calculations and your measurements with lab instructor.

4 Thermal resistance noise

With this amplifier it is easy to study the thermal noise (Johnson noise) of a resistance.

Voltage fluctuations across a resistorRat the absolute temperatureT is a Gaussian white noise called thermal noise or Johnson noise. The rms noise voltage is given by the Johnson-Nyquist formula:

v_n,R=√

4kT Rin V/√ Hz,

wherekis the Boltzmann constant:k = 1.380×10⁻²³J.K^-1

A resistance can be replaced by a noiseless resistanceR^∗with a noise voltage generator of rms valuev_n,Ras represented in the figure 1.4.

vn ,R

R

R^✶

Figure 1.4: Resistance thermal noise model

The low noise amplifier studied previously can be used to study the thermal noise of a resistor connected between the amplifier input and ground.

4.1 Influence of the resistance

With the spectrum analyzer, measureP_{@1 Hz}(200 kHz)indBm(output noise PSD at the frequency of200 kHz) for different resistors connected to the amplifier input.

Q7 Deduce the amplifier rms voltage output noise, vn,out(200 kHz), for these resistances (fill up the table started at questionQ4).

At the entrance of the amplifier, we have two sources of noise,

• the amplifier noise, measured at questionQ5,

• the resistance thermal noise.

We can represent these two noises by two white noise generators placed at the input of the amplifier (figure 1.5).

These sources are statistically independent. Therefore, the total noise power is the sum of the powers of these two noise generators.

G ,f vn ,ampli

vout

R^✶ vn ,R

Figure 1.5: Model of the thermal noise of a resistance, at the input of a noisy amplifier.

Q8 With Excel, deduce from the previous measurements the rms noise voltage normalized at1 Hz,vn,Rof the thermal noise for each resistance.

Do not forget to take into account the noise of the amplifier.

Q9 Trace on the same graph the curvesv_n,R = f√ R

deduced from your measurements and from calculation using the Johnson-Nyquist for- mula.

Q10 Observe the noise voltage output of the amplifier for a larger fre- quency span from0to2 MHzwhen you increase the value ofR. Can you explain what you see? Deduce why the measured noise is different from the theoretical noise for the high resistance values.

Q11 Comparing the theoretical and experimental slopes for the small values of resistance, evaluate the systematic error measurement in dB probably due to a calibration default of the spectrum analyzer.

Important To take into account and therefore correct this error later in the lab, keep the same settings of the spectrum analyzer.

5. PHOTON NOISE 11

4.2 Influence of the temperature

To measure the influence of the temperature, you will put a resistance (protected in a box) in liquid nitrogen and thus compare the noise at room temperature and at liquid nitrogen temperature. This simple experiment shows the principle of a noise thermometer by measuring the thermody- namic temperature.

Connect the resistance protected by a small metal box to the ampli- fier input.

Q12 Measure, using the spectrum analyzer, P_{@1 Hz}(200 kHz) in dBm, PSD of the output noise at a frequency of200 kHz, when the resistance is at room temperature. Deduce the rms noise voltage normalized at1 Hz, vn,R,T₁.Do not forget to take into account the noise of the amplifier.

Q13 Repeat this measurement when the resistance is placed in liquid nitrogen. Deduce the rms noise voltagevn,R,T₂ at this temperature. Use this measurement to deduce the temperature of liquid nitrogen as accu- rately as possible.

5 Photon noise

The photon noise is related to the statistical fluctuations of the photons collected by the photodetector. The photon counting statistics is known to be Poissonian: if the detector surface receivesN photons in average during an integration time τ, the standard deviation of the number of photons received is√

N .

The photoelectrons created in the detector obey the same Poissonian statistics and this explains the shot-noise (often called photon noise) on the photocurrent. The average photocurrent isI_phand the variancei²_n,phof the fluctuations is given by the Schottky formula:

in,ph=p

2eIph(in A/√

Hz) whereeis the electron chargee = 1.6×10⁻¹⁹C A photodiode (detecting a Poissonian flux of photons) can be repre- sented by a DC current generator I_ph, in parallel with a current noise generator:

in , ph

Iph

Figure 1.6: Photodetection noise model.

This current noise will be amplified by the circuit of the figure 1.7 :

anode cathode

battery : +24V

Iphot photodiode

amplifier Vs

Rc=330

R=100

Ω Ω

Amplifier : "photon noise"

1uF DC Voltmeter

low noise

Figure 1.7: Amplifier : "photon noise"

The DC component of the current I_ph passes through the two resis- tancesR₁andR₂.We can deduce its value from the measurement of the voltageV acrossR₂(100 Ω):I_ph=V /R₂. The photodiode is reverse biased with24 VDC supplied by a battery (noiseless).

Connect the photodiode and the battery. Place the photodiode in front of a white light source which intensity is adjustable. The photodiode is an E.G.G.C30809photodiode whose quantum efficiency is0.83at900 nm (datasheet in appendix).

A voltmeter connected to the output Iphotof the box measures the DC photonic current delivered by the photodiode.

Check the average photocurrent increases with the flux received by the photodiode (do not go above10 mA,1 Von the voltmeter).

Observe the noise output voltage of the amplifier using the oscillo- scope and the spectrum analyzer when increasing the flux.

5. PHOTON NOISE 13 Q14 Observe the output noise for a span from0 to2 MHz. Is the shot noise a white noise? How is it varying with the flux received by the pho- todiode?

Q15 Measure, using the spectrum analyzer, P_{@1 Hz}(200 kHz) in dBm, PSD of the output noise at a frequency of 200 kHz, for different aver- age photocurrents I_ph from 0 to 10 mA. Deduce the rms noise voltage v_n,out(200 kHz)for these values ofI_ph.

At the entrance of the amplifier, we have now three sources of noise:

• the photon noisevn,ph=R1·in,ph,

• the resistance(R1= 324 Ω)thermal noise,vn,R₁,

• and the amplifier noise,v_n,ampli.

Note that theR2 resistance is not taken into account here because it is short-circuited by the capacitor in parallel. The complete noise model of the photodetection is given by the circuit in Figure 1.8:

G ,f vn ,ampli

vout

R1

✶=324

vn ,R1

in , ph

G ,f vn ,ampli

vout

R1

✶=324

vn ,R1

vn , ph

Figure 1.8: Photodectection noise model.

These noise sources are statistically independent. So their noise pow- ers can be summed in order to find the total noise power:

v²_n,tot =v²_n,R1+ (R1·in,ph)²+v²_n,ampli(vn,tot in V/√ Hz)

The noise measurement whenIph = 0 mAgives the measurement of the amplifier and thermal noises.

Q16 Determine the value of the amplifier gain at a frequency of200 kHz from the Bode diagram of the amplifier given in Appendix, deduce the voltage noise at the input of the amplifier:vn,tot.

Q17 With Excel, calculate the rms noise current in,ph taking into ac- count the systematic error determined in questionQ11.

Q18 Plot:i_n,ph=f p I_ph

. Compare with the values given by the Shot- tky formula.

Q19 Evaluate the uncertainty if the uncertainty on the displayed noise value is0.3dB.

Check your calculations and your measurements with the lab in- structor.

6 Noise reduction

This last part presents a way to measure a photocurrent with a noise power below the shot-noise limit. This experiment will prove that the photodetector is not responsible for the shot-noise. Shot-noise is related to the quantum nature of light and the shot-noise limit is due to the Pois- sonian statistics of the collected photons. This experiment will show that a suitable light source can give a sub-Poissonian statistics of photons col- lected and consequently leads to a reduction of noise.

The idea is here to use, as a light source, a high quantum efficiency light-emitting diode (HamamatsuL2656whose quantum efficiency is about 0.15photons per electron at center wavelength of 890 nm). We put this LED as close as possible to the photodiode (E.G.G. C30809) to collect the largest number of photons we can (we took off the window of the pho- todiode, and both the LED and the photodiode are in a metal box).

The figure below explains the principle of the shot-noise reduction ex- periment:

6. NOISE REDUCTION 15

+24V Poisson current

source

Constant current source

R

Ampli 1 R

100Ω 100Ω

Measurement of Iph

Measurement of Iled

Measurement of the noise on the current Iph

LED Photodiode

switch

Figure 1.9: Principle of the shot-noise reduction experiment Figure 1.10 represents the circuit which drives the LED either with a very low noise current produced by an usual stabilized power supply (KIKUSUI) or with a “Poissonian” current produced by three photodiodes illuminated by an ordinary white light source. Changing the light level will change the mean current through the LED. It is easy to adjust the stabilized power supply and the light level in a way to get exactly the same mean current in the LED. This current, I_LED , is measured by a voltmeter in parallel with the200 Ωresistance.

LED anode

cathode

GBF alimentation stabilized +24V

photodiodes

switch

C=22nF

100k 330

100 to Amplifier 1

(I led)

Ω Ω Ω

1kΩ

to DC voltmeter (I led noise)

Figure 1.10: Setup of the sub-Poissonian/Poissonian light emitting device

6.1 Connecting the circuit

Replace the photodiode of the previous part by the photodiode which is in the small box “photodiode + LED”.

Connect a second voltmeter at theILEDoutput to measure the aver- age current in the LED. Connect the stabilized power supply and the bias voltage polarization for the 3 photodiodes (24 V) to the commutation box.

Do not connect anything to the input “GBF”.

Put the switch on the “stabilized power supply” position and adjust the photocurrent in the photodiode at exactly3 mA.

Put the switch on the “Poisson current” position, and adjust the flux on the 3 photodiodes in order to get the exactly same photocurrent (3 mA) in the photodiode.

6.2 Measurement

Q20 Measure the current in the LED and deduce the total quantum efficiencyηT,i.e.the number of electrons delivered by the photodiode per second divided by the number of electrons crossing the LED per second.

Q21 With the spectrum analyzer, measureP_{@1 Hz}(200 kHz)indBm. Check that you find exactly the same value as in the previous part (Q15). This proves you are at the shot noise level.

Q22 Deduce the rms noise currentin,ph.

Switch to the “stabilized power supply”position. Check that the DC current is stillIph= 3 mA.

Q23 Measure P_{@1 Hz}(200 kHz) in dBm. Deduce the rms noise current i_n,ph.

Q24 What noise reduction (in dB) do you find?

Q25 Compare to the value calculated as explained in the next para- graph.

6. NOISE REDUCTION 17 To obtain a better visualization of the noise reduction, you can display the spectrum on5dB/div scale. Then you can average the spectrum on the

“Poissonian current” position and save it. At last, average the spectrum on “stabilized power supply” position and save it.

Ask the lab instructor how to use the average function of the spec- trum analyzer.

6.3 Simple explanation of the noise reduction

When a constant current source is used to drive the LED, the noise on the current is very low. The fluctuations of the number of electrons crossing the LED are very low in comparison with a “Poissonian statistics”. If the quantum-efficiency of the LED was equal to one, the fluctuations of the number of photons emitted by the LED and collected by the photodiode would be very low too. The resulting noise reduction would be very large.

Unfortunately, the total quantum efficiency,ηT = η_PhD·η_LED, is only about 0.17. This means that for six electrons crossing the LED only one electron on average will be generated by the photodiode.

If we suppose that the current in the LED is noiseless, the number of electrons through the LED,N_e,LED, during a timeτ, is constant. The number of electrons generated by the photodiode during a timeτis thus given by a binomial distribution. The mean value and the variance of the number of electrons crossing the photodiode during a timeτare:

Ne,photodiode=ηTN_e,LED and:

σNe,photodiode = q

ηT(1−ηT)N_e,LED This leads to:

I_ph= Ne,photodiode

τ e =η_TN_e,LED

τ e =η_TI_LED, and the rms valuei_rms,phof this photocurrent:

i_rms,ph= σNe,photodiode

τ e = r

ηT(1−ηT)N_e,LEDe² τ² The bandwidth isδf = 1/2τ,so the photocurrent noise is:

i_rms,ph= q

2eIph(1−ηT)δf (in A)

instead of

i_rms,ph=p 2eI_phδf

for the shot noise. Thus, the noise power reduction is:

P_reduced

P_photon = 1−ηT

In dB:

Preduction,dB=Preduced,dBm−P_photon,dBm= 10 log (1−ηT)

7 Short guidelines for the redaction of the report

For the report, please do not answer all the questions of the text linearly and do not describe all your experimental procedures. Please explain for all three configurations what are the contributions to the noise, their nature and their rms levels. A particular attention will be paid to the graphs in Parts "Thermal resistance noise" (influence of the resistance) and "Photon noise". Thus, We expect you to establish a brief overview of the noise levels in the different setups under study. Redaction of the last part "Noise reduction" is optional, but will be strongly taken into consideration if satisfying.

References on noise reduction

[1] Introduction à la réduction du bruit quantique. S. Reynaud Ann. Phys. Fr. 15, 63 (1990).

[2] Sub-Shot-Noise Manipulation of Light Using Semiconductor Emit- ters and Receivers. J.-F. Roch, J.-Ph. Poizat and P. Grangier

Physical Review Letters Vol 71, Number 13 (1993)

7. SHORT GUIDELINES FOR THE REDACTION OF THE REPORT19

Appendix 1. Bode diagrams of the amplifiers

10⁴ 10⁵ 10⁶

32 34 36 38 40 42 44 46 48

Frequency (Hz)

Gain(dB)

Amplifier1- Thermal resistance noise

10⁴ 10⁵ 10⁶

32 34 36 38 40 42 44 46 48

Frequency (Hz)

Gain(dB)

Amplificateur2- Photon noise

Appendix 2. The spectrum analyser

VariableGain f0-f0

Pass BandFilter f0-f0RBW

Local oscillatorVariable f0 LOG Ampli.

Video filter VerticalscalelineardB Horiz. scanSPANCenter frequencysetting

Channel YChannel XSweep

R F S pe ctr um A na lyze r

REF levelSettingResolutionBandwidth settingRBW 500 Hz to 5 MHz

P dBm

Fre qu enc y Sc re en

Ref level

B 2

Infrared detector characteristic

measurement

Version: February 5, 2019 You should read carefully this text and prepare the questions P1- P12 before the lab.

Data analysis have to be done and checked during the lab session.

Contents

1 Objectives . . . . 21 2 Detector characteristics . . . . 22 3 Measurements . . . . 27 4 Analysis of the measurements . . . . 33 5 Writing down the report . . . . 34 Appendix 1 - Black body spectral radiance . . . . 36 Appendix 2 - Atmospheric transmittance . . . . 36 Appendix 3 - Spectral detectivity . . . . 37 Appendix 4 - Fast Fourier Transform and windowing . 37

1 Objectives

At the end of the session lab, you will be able to:

21

• measure the performance of an infrared detector, which means be- ing able to:

– identify the relevant parameters (dark current, quantum effi- ciency, black-body response, noise , detectivity);

– identify the specificities of the IR domain (black-body radiation, ambient background, dark current of the detector);

– use a digital spectrum analyzer and understand the need for an antialiasing filter and an appropriate window;

– understand the rational behind the use of a chopper;

– be able to compute the etendue of the measurement setup;

– evaluate the uncertainty of each measurement;

• propose a measurement procedure that can be used to verify if an IR detector is limited by the background photon noise (BLIP).

During this lab, we will therefore measure the characteristics of an IR detector cooled to77 Kby liquid nitrogen.

The detector is anInSbphotodiode(sensitive in the 3–5 microns spec- tral band), with model referenceP5968-100 Hamamatsu. The diameter is1 mmand the total angle of view is60^◦.

The full characteristics of the detector can be found online:

http://jp.hamamatsu.com

This lab will provide an opportunity to apply concepts learnt in the course of photometry and detectors noise, and to familiarize with conven- tional experimental techniques. Measurements are relatively simple and fast, but they must be understood and analyzed with care.

P1 For which applications, one may use infrared detectors? Give at least 3 examples. Describe the different families of infrared technologies and give their specificities.

2 Detector characteristics

2.1 Spectral response of a photonic detector

The spectral responseR(λ)of a photodiode detector is defined for a sta- tionary monochromatic fluxΦ_λ,

R(λ) =I_ph Φλ

in A/W,

2. DETECTOR CHARACTERISTICS 23 whereI_phis the mean current across the photodiode.

A photodiode is a quantum detector,i.e.a photon counter. So the cur- rent in the photodiode is easily related to the number of photons received per second,n_ph,λ,

I_ph=η(λ)·n_ph,λ·e,

whereeis the electron charge andη(λ)is the quantum efficiency (photon to electron conversion).

P2 Show that the spectral response of the detector is given by R(λ) =I_ph

Φλ

= λ·η(λ)·e

h·c in A W, wherehis the Planck constanth = 6.626×10⁻³⁴J s.

We also define therelativespectral response of the detector:

S(λ) = R(λ)

maxR(λ) = R(λ) R λ_peak

P3 Explain why, if the quantum efficiency is constant, the spectral re- sponse S(λ) forλ < λ_peak is a linear function as represented on Figure 2.1.

₀ _pic



1

₀ _pic S

1

Figure 2.1: Spectral responsivity.

We will study an InSb detector whose cut off wavelength is: λc = 5.5µm.

The value corresponding to the peak of sensibility isλ_peak= 5.3µm.

P4 Calculate the maximal response R(λ_c) of a InSb detector at λ_c = 5.3µmassuming the quantum efficiency is equal to1.

The relative spectral response of the studied detector is obtained by comparison with a detector which spectral response is well known. For this purpose, one may use a pyroelectric detector as a reference. It is a thermal detector that has a constant spectral response. Some previous measurements are available on the computer.

See filesensibilite_relative_insb.xls.

2.2 Background infrared radiation

For IR detectors, the background photon flux detected is generally very large compared to the flux (signal) we want to measure (this explains why we need a chopper in front of our source in our setup). The black body emission of the whole scene at room temperature viewed by the detector is responsible for this large flux of background photons. This flux will be converted in a DC current,I_ph,BG. To determine this current, one needs to calculate the flux of background photons using Planck photonic black body law.

P5 Show that if the FOV (Field Of View) of the detector is2α, the flux of photons received by the detector is:

nph,BG=πAdsin²α·L_ph,BG(in s⁻¹),

whereAdis the area of the detector, andL_ph,BGis the photonic total radi- ance between2and5.5µm,

L_ph,BG=

5.5µm

Z

2µm

dL_ph dλ

^TBG

dλ(in s⁻¹m⁻²sr⁻¹).

The spectral photonic radiance is given by dL_ph

dλ ^T

= 2c λ⁴

1 e

hc λkT −1

(2.1)

wherehis the Planck constant (h= 6.626×10⁻³⁴J s) andkis the Boltz- mann constant (k= 1.38×10⁻²³J K⁻¹).

P6 Calculatenph,BGfor our detector (the diameter is1 mmand the half angleα= 30^◦) if we assume that the quantum efficiency is1on the wave- length range2−5.5µm. Calculate the corresponding DC currentIph,BG.

2. DETECTOR CHARACTERISTICS 25 The total photonic radiance has to be calculated by integration of the spectral photonic radiance (2.1) on the wavelength range2−5.5µm. This integration can be done numerically withMatlaborExcelor using the webpage: http://www.spectralcalc.com/blackbody_calculator/blackbody.php

2.3 Background photon noise limit

The fluctuation of this flux of background photons is generally the main source of noise for IR detectors (these detectors are Background Limited Infrared Photodetectors or "BLIP") .

In this case, the noise current measured in a1 Hz equivalent Band- width is given by the Schottky formula :

in,BG=p

2eIph,BG(in A/√ Hz)

P7 Deducei_n,BGfrom the currentI_ph,BGcalculated in questionP6.

2.4 N.E.P.: Noise Equivalent Power

The Noise-Equivalent Power (NEP) is the radiant power that produces a signal-to-noise ratio of unity at the output of a given optical detector at a given modulation frequency, operating wavelength, and equivalent noise bandwidth.

NEP (λ) = ∆Φ_pp(λ) =i_{noise, rms} R(λ) in W

In other words the N.E.P. gives the smallest detectable variation of IR flux.

P8 Explain why the NEP is proportional to the square root of the effec- tive bandwidth.

P9 For a BLIP detector, explain why the NEP is proportional to the square root of its surface?

Because the NEP is proportional to the square root of the detector sur- face and to the square root of the ENBW (Equivalent Noise Band Width), in order to compare different IR detectors we have to define the ratio:

NEP (λ)

√A_d√

∆f

whereA_dis the detector area and∆fis the Equivalent Noise Band Width ENBW.

2.4.1 Spectral Detectivity

The detectivity, preferred by the manufacturers, is the inverse of the quantity defined above because the higher the detectivity, the better the detector is:

D^∗(λ) =

√Ad

√∆f

NEP (λ) =R(λ)

√Ad

√∆f

i_{noise, rms} =R(λ)

√Ad

inoise, rms.@1Hz

whereinoise, rms.@1Hz is expressed inA/√

Hz,D^∗(λ)incm√

Hz/W,as the detector area is expressed incm².

The maximal value is obtained forλpeak and is called peak detectivity (D^∗_peak).

P10 What is the value ofD^∗_peak according to the datasheet ?

2.5 Black body Detectivity

A direct measurement of the spectral detectivity versus the wavelength is difficult. So we will first measure the Black Body Detectivity (the de- tector is illuminated by a black body at500 K). Then we will measure the relative spectral response of the detectorS(λ).

The Black Body DetectivityD_BB^∗ (T_BB, f,∆f)is:

D^∗_BB(T_BB, f,∆f) =R_BB

√A_d√

∆f inoise, rms.(f)

= I_ph Φ_BB,TBB

√Ad

inoise, rms.@1 Hz(f) incm√

Hz/W, whereT_BBis the black body temperature,f the modulation frequency and∆f the ENBW.

P11 For which values ofT_CN, f,∆fis the black body detectivity given in the datasheet?

Remark From the measurements ofD^∗_BB(T_BB, f,∆f)andS(λ)we will deduceD^∗(λ)for this detector (see paragraph 4).

3. MEASUREMENTS 27

3 Measurements

The circuit diagram is given in Figure 2.2.

+ -

Ip h

Detector

DC Output

Output

- +

R_C

V₀

Current to voltage converter + adjustable gain

Figure 2.2: Circuit diagram.

P12 What is the name of the first stage of the detection circuit? What is the link between V0 andIph? What is the bias voltage? What is the function of the second amplier? How about theRCfilter between the two amplifiers?

3.1 Measurement of the current due to the background infrared radiation

Connect the detector to the amplifier box and the voltmeter to theDC output.Connect the output to the oscilloscope.

Pour slowly and carefully liquid nitrogen into the cryostat and wait for the signal apparition.

Q1 Measure the DC voltage. Deduce the value ofIph,BGand, compar- ing it with the value determined at question P6, estimate the average quantum efficiency of the detector.

3.2 Measurement of the detector noise

Connect the output of the amplifier box to the filter box.

3.2.1 Noise measurement with an oscillloscope

Display the signal on theRIGOL oscilloscope. Choose properly the value ofRc and of the different gains in order to obtain a correct signal amplitude without any saturation.

Q2 Where does this noise come from? Assuming this noise is Gaus- sian, measureV_noise,rmswith the oscilloscope (you can use the theoretical framework provided by the subject of Labwork 9, and we remind you that V_noise,rms=V_pp/6for a Gaussian noise).

Q3 The bandwidth of the anti-aliasing filter is about2 kHz. Assuming the noise is a white noise on this bandwidth, calculatevnoise,rms@1Hz in a 1 Hzanalysis bandwidth (rms noise voltage inV/√

Hz). Deduce the cur- rent noise,inoise, rms.@1Hz , in the photodiode for an equivalent bandwidth of 1 Hz(current noise normalized inA/√

Hz). Compare to the value ob- tained in preparation (P7).

3.2.2 Accurate noise measurement with a FFT spectrum ana- lyzer

Connect the signal on the 1^stinput channel of theLeCroyanalyzer.

Upload the setup file namedTPDetIR HistBruit. To do so, go to the menuFile>Recall Setup.

Click on theC1yellow frame, located just below the plot area. Check that the coupling parameter is set toDC1MΩ. Change the parameter value if needed.

Q4 Can we consider that the noise measured by the analyzer is Gaus- sian? Explain why this approximation is physically relevant.

Now, upload the setup file namedTPDetIR TFBruit in the menu File>Recall Setup. Check that the coupling parameter is still set to the correct value.

Q5 Is the measured noise a white noise? Was it expected?

3. MEASUREMENTS 29 Q6 Explain the role of the anti-aliasing filter. Where do you see its influence? Why is it necessary for this measurement? How should we choose the sampling frequency?

The background photon noise (detector noise) and the amplification noise are both responsible for the measured noise. These noise sources are statistically independent so:

v_total,rms=q

v_noise,rms² +v²_ampli,rms

Go to the Cursorsmenu and selectHorizontal Abs. Display the cursor settings in Cursors>Cursor Setup and select Hz as the X - axisparameter. The x-coordinate (frequencies) of the cursor is displayed on the right of the screen, its y-coordinate is displayed in the red and blue frames intitledF1andF2respectively. We remind you thatP_dBm = 10 log _1mW^P

whereP =V²/1MΩ.

Q7 Measure the noise voltage at the ouput for 500 Hz. Then, for the same frequency, measure the noise voltage at the output when the detec- tor is disconnected. Deduce the detector noise voltagev_noise,rms and the current noise of the detectori_noise,rms.

Q8 Note the value of the equivalent noise bandwidth∆f displayed in theFFTpanel that appears when you click on de redF2frame. Deduce the noise current of the detector in1Hzbandwidthinoise,rms@1Hz. Compare to the value obtained in preparation (P 7). Is the detector BLIP?

3.3 Measurement of the black body response of the IR detector

To measure the black body response of the IR detector, R_BB= ∆I_ph

∆Φ_BB in A/W we will have to:

• determine precisely the flux variation received by the detector,

• measure carefully the photocurrent induced by this flux variation.

3.3.1 Set-up

Current to voltage amplifier IR Detector

Black body (500 K) Chopper

Diaphragm

Oscilloscope Data acquisition Anti-aliasing filter

Figure 2.3: Set-up

When the chopper is turning, the detector sees through the diaphragm alternately a black blade at room temperature or the black body at500K.

Do not change the temperature settings of the black body!

3.3.2 First measurement using an oscilloscope Set the modulator frequency to500Hz.

Place the detector precisely at 1 meter from the diaphragm (Detector is at(9±1)mmbehind the window).

Align carefully the Black Body, the diaphragm (we will choose a di- ameterφ = 5 mm) and the detector.

Optimize the signal by improving your alignment.

Q9 Measure the peak to peak voltage without anti-aliasing filter.

The flux variation∆Φ(t)is periodic and can thus be decomposed as a Fourier series. One can then calculate the RMS value of its fundamental

3. MEASUREMENTS 31 component∆Φ_rms. One can show that RMS value is related to the peak to valley of the flux variationΦ_ppby the Modulation Factor (M.F.):

MF = ∆Φ_rms

Φ_pp = ∆Φ_rms Φmax−Φmin

(2.2)

W d

Φmax

Φmin

Φ(t)flux variation

Modulator t

W : length of the arc between 2 blades in front of the diaphragm d: diaphragm diameter

Figure 2.4: Chopper For a square signal (cased << W):

MF =

√ 2 π = 0.45

Q10 Show that the modulation factor for a square signal is:

MF = ∆V_rms,500 Hz

Vpeak to peak

=

√2 π = 0.45 Deduce a value of∆V_{rms,500 Hz}.

Q11 Deduce a value of∆IBB, rms,500 Hz.

3.3.3 Measurement of the signal obtained by the FFT method Add the anti-aliasing filter (low-pass filter, cut-off frequency of2 kHz) and connect the output signal to theLeCroyanalyzer.

Go to the menu File>Recall Setupand upload the file TPDetIR TF Signal. The P2 measurement channel gives the amplitude of the highest peak, the one at500Hz.

Q12 Measure the RMS voltage after the filter at500Hz.

Vary slightly the chopping frequency with an amplitude of±20Hz.

Q13 Note the effective value of the highest peak measured by the ana- lyzer during this variation. Explain the origin of these fluctuations. What is the influence of the acquisition window, the sampling frequency,Fe, and the influence of the number of acquired pointsNe? Explain why the “flat top” window is theoretically well fitted for this kind of measurement (you can use the appendix for your explanations).

Set back the frequency to 500Hz. In theFFT panel of F2 channel, select theFlat Topwindow.

Q14 Measure the amplitude of the500Hzpeak. Knowing the gain of the amplifier and of the filter (inV/A), measure the current,∆IBB, rms,500 Hz

through the photodiode. Evaluate the accuracy of this measurement.

Check your result with the lab instructor.

3.3.4 Determination of the flux variation received by the IR de- tector

Calculation of the peak to peak flux variation

Q15 Measure the diaphragm - detector distance and calculate the etendue between the detector and the diaphragm (the InSb detector diameter is 1 mm).

The black body radiance follows the Stefan law:

L= σT⁴ π

withσ= 5,67.10⁻⁸W/m².K⁴

Q16 Calculate the peak to peak flux variation received by the IR detec- tor∆Φ_BB,pp.

Calculation of the effective variation of the flux received by the detector

Q17 Using Eq. (2.2), calculate∆Φ_{rms,500 Hz}received by the detector.

4. ANALYSIS OF THE MEASUREMENTS 33 3.3.5 Black body response of the detector

Q18 Calculate the black body response of the IR detectorR_BB= _∆Φ^∆Iph

BB

Check your result with the lab instructor.

3.3.6 Calculation of the black body detectivity

Q19 Deduce the black body detectivity D^∗_BB(T_BB, f,∆f). Evaluate the accuracy of your measurement.

The detector noise is normally mainly due to the photon noise of the ambiant photons. In this case, the noise of the detector depends on the field of view (FOV).

Q20 Explain why the noise of the detector depends on the FOV. How shouldD^∗_BB(T_BB, f,∆f)be corrected to be compared with a2πsteradian detector?

4 Analysis of the measurements

In this section, no measurement is required. However, you will need the filesensibilite_relative_insb.xlswhich is saved on the computer of the room. Do not forget to make a copy of the file.

Spectral Response and spectral detectivity

With the measurements of the black body Response,R_BBand the relative spectral Response, the spectral response can be deduced:

γ=R λ_peak R_BB

The photonic current is given by

∆I_ph =R_BB∆Φ_BB with :

∆Φ_BB= MF×σ

π T_BB⁴ −T_BG⁴ U

where U is the etendue, MF is the modulation factor, BB refers to the blackbody temperature and BG to background temperature.

E1 Explain why the photonic current can also be calculated by integra- tion of the black body radiance :

I_ph = MF×U× Z ∞

0

R(λ) dL

dλ TBB

BB

− dL

dλ TBG

BG

! dλ

= MF×U×R λ_peak Z ∞

0

S(λ) dL

dλ ^TBB

BB

− dL

dλ ^TBG

BG

! dλ

where_dL

dλ

^TBB

BB and_dL

dλ

^TBG

BG are the spectral radiances of the black body at temperature atT_BBandT_BG, given by :

dL dλ

^T

BB

= 2hc² λ⁵

1 e

hc λkT −1 whereλexpressed inm, ^dL_dλ in W ·m⁻² ·sr⁻¹

/m E2 Deduce the ratioγ:

γ=

σ

π T_BB⁴ −T_BG⁴ R∞

0 S(λ) dL

dλ

^TBB

BB −dL dλ

^TBG

BG

dλ

E3 Perform this calculation using Excel.

E4 Calculate R(λ_peak) and give the representation of the spectral Re- sponseR(λ). Plot also the spectral quantum efficiency curve.

E5 Usingγ, calculateD^∗_peak =D^∗(λ_peak)and plot the spectral detectiv- ity curveD^∗(λ).

5 Writing down the report

In your report, you do not have to linearly describe your measurement protocols and your results. However, you should write a well structured document (between 2 and 6 pages maximum with an introduction, a con- clusion, several parts, etc.) where you will summarize:

• the major concepts related to the technology you studied in the lab- work,

5. WRITING DOWN THE REPORT 35

• the key points and challenges of the characterization of an IR detec- tor,

• your conclusions of the performance of the detector you studied dur- ing the labwork.

Your comments should be based on your measurements. You may also compare your observations on the infrared technology with what you know about sensors in the visible range.

Appendix 1 - Black body spectral radiance

Figure 2.5: Black Body spectral radiance

Appendix 2 - Atmospheric transmittance

Figure 2.6: Atmospheric transmittance

5. WRITING DOWN THE REPORT 37

Appendix 3 - Spectral detectivity

Figure 2.7: Spectral detectivities of IR detectors

Appendix 4 - Fast Fourier Transform and win- dowing

Let’s take the example of a square signal,s(t), which frequency is f = 100 Hz(T = 10 ms). This signal is digitized at a sampling frequency,Fe= 1 kHz(Te= 1 ms). We useNeacquired points .

s(t)

t T

NeTe Fenêtre temporelle :

square wave signals(t)

The signal,s(t), is periodic, so its spectrum is represented by :

Spectrum ofs(t)

Windowing

The temporal window is rectangular, its length isN_eT_e, and its Fourier Transform is a sinc function:

Spectrum of a rectangular window of lengthN_eT_e

So, the spectrum of the signal limited by this rectangular window is given by the spectrum of the periodic signals(t)convoluted by this sinc function :

Spectrum ofs(t)in a rectangular window.

Sampling

The spectrum of the sampled signal is also a periodic spectrum with a period Fe = 1/T e. This may produce aliasing. This is the reason why a low pass filter is needed with a cut-off frequencyf c < Fe/2.

5. WRITING DOWN THE REPORT 39

Sampled signal spectrum

FFT Algorithm

Fast Fourier Transform algorithm uses exactly the same number,Ne, in the frequency domain as in the time domain. A FFT calculateN_epoints of the spectrum between0 and F_e. So the spacing between 2 points is

∆f = _N^Fe

e.

Knowing that the width of the sinc function for a rectangular window is2/NeTe, you realize that the FFT algorithm calculates only 2 points on the sinc function main lobe. This will produce a very important measure- ment error on the calculation of a periodic signal spectral component am- plitudes. And this error will not depend on the number of sample points Ne you choose. This error may be 36% of the real amplitude (case b). The amplitude is well calculated only in case c, when the signal is a multiple of∆f :

cases a/b/c

To avoid this error, the usual solution is to take a different temporal window. We should choose a window which is at least larger than^F_N^e

e. This is the case for the "Flat Top" window (see windows and corresponding spectrum at the end of this appendix). So the sampled periodic signal is multiplied by a "Flat Top" window before the FFT is calculated..

ENBW : Equivalent Noise Band Width

For noise analysis any window will be suited, but the ENBW is

Temporal Window Leakage Max error on the amplitude ENBW

Rectangular -13dB : 0.224 36% _N^Fe

e

Von Hann -32dB : 0.025 15% 1.5×_N^Fe

e

Hamming -43dB : 0.0070 18.5% 1.37×_N^Fe

e

Blackmann-Harris -67dB : 0.00045 12% 1.71×_N^Fe

e

Flat-Top -44dB : 0.0063 0.1% 2.91×_N^Fe

e

Temporal windows are calculated by : w_k =a₀+a₁cos

2πk N_e

+a₂cos 4πk

N_e

withk= 0, ..., N_e−1 Temporal window a0 a1 a2

Rectangular 1.0 0.0 0.0

Von Hann 0.5 -0.5 0.0

Hamming 0.54 -0.46 0.0

Blackmann-Harris 0.423 -0.497 0.079 Flat-Top 0.281 -0.521 0.198

B 3

CMOS sensor

Version: February 5, 2019 Questions from P1 to P5 should be prepared before the session.

Contents

1 Introduction . . . . 41 2 Preliminary questions . . . . 43 3 Matlab interface and sensor learning . . . . 44 4 Measurement of the read-out noise . . . . 46 5 Study of the dark signal . . . . 46 6 Study of the sensor linearity and photon noise . . 47 7 Measurement of the sensor spectral response . . . 50 8 Synthesis . . . . 51

1 Introduction

In 2014, 95 % of the manufactured cameras were CMOS (Complementary Metal Oxyd Semiconductor) cameras, and only 5 % were CCD (Charge- Coupled Device) cameras. The main difference between the two technolo- gies is that each pixel of a CMOS sensor possesses its own read-out circuit (charge-voltage converter and amplifier), directly next to the photosensi- tive area. Compared to the CCD technology, the benefits of the CMOS technology are:

• Sensors easier to produce and thus cheaper,

• Low consumption,

41

• Faster data reading,

• Each pixel can be individually controlled,

• Possibility to do image processing directly at the sensor level (defi- nition of regions of interest (ROI), binning, filtering, . . . )

The drawbacks of the technology are a lower dynamic range and a higher noise level.

Figure 3.1: Left - CMOS e2V sensor studied during this session. Right - diagram of the general principle of CMOS sensors.

The goal of this session is to measure the characteristics of an in- dustrialµEye camera, equipped with a CMOS sensor, manufactured by e2V (1.3 Mpixels, 5.3×5.3µm² pixels). Figures 3.2 and 3.3 show some characteristics of the sensor. We are specifically interested in the sensor linearity, the read-out noise, the dark signal and the photon noise. The measured values will be compared to the data given by the manufacturer.

Figure 3.2: Extract from the CMOS e2V sensor datasheet - spectral re- sponse.